This paper discusses a multimodal density function estimation problem of a random vector. A comparative accuracy analysis of some popular non-parametric estimators is made by using the Monte-Carlo method. The paper demonstrates that the estimation quality increases significantly if the sample is clustered (i.e., the multimodal density function is approximated by a mixture of unimodal densities), and later on, the density estimation methods are applied separately to each cluster. In this paper, the sample is clustered using the Gaussian distribution mixture model and the EM algorithm. The highest efficiency in the analysed cases was reached by using the iterative procedure proposed by Friedman for estimating a density component corresponding to each cluster after the primary sample clustering mentioned. The Friedman procedure is based on both the projection pursuit of multivariate observations and transformation of the univariate projections into the standard Gaussian random values (using the density function estimates of these projections).
Background and objectives: Many studies have been carried out on the negative health effects of exposure to PM10, PM 2.5, NO2, CO, SO2 and B[a]P for small populations. The main purpose of this study was to explore the association of air pollution to diagnosis of asthma for the whole huge population of school children between 7–17 years in Vilnius (Lithuania) using geographical information system analysis tools. Material and Methods: In the research, a child population of 51,235 individuals was involved. From this large database, we identified children who had asthma diagnosis J45 (ICD-10 AM). Residential pollution concentrations and proximity to roads and green spaces were obtained using the ArcGIS spatial analysis tool from simulated air pollution maps. Multiple stepwise logistic regression was used to explore the relation between air pollution concentration and proximity between the roads and green spaces where children with asthma were living. Further, we explored the interaction between variables. Results: From 51,235 school children aged 7–17 years, 3065 children had asthma in 2017. We investigated significant associations, such as the likelihood of getting sick with age (odds ratio (OR) = 0.949, p < 0.001), gender (OR = 1.357, p = 0.003), NO2 (OR = 1.013, p = 0.019), distance from the green spaces (OR = 1.327, p = 0.013) and interactions of age × gender (OR = 1.024, p = 0.051). The influence of gender on disease is partly explained by different age dependency slopes for boys and girls. Conclusions: According to our results, younger children are more likely to get sick, more cases appended on the lowest age group from 7 to 10 years (almost half cases (49.2%)) and asthma was respectively nearly twice more common in boys (64.1%) than in girls (35.9%). The risk of asthma is related to a higher concentration of NO2 and residence proximity to green spaces.
This paper discusses a soft sample clustering problem for multivariate independent random data satisfying the mixture model of the Gaussian distribution. The theory recommends to estimate the parameters of model by the maximum likelihood method and to use "plug-in" approach for data clustering. Unfortunately, the calculation problem of the maximum likelihood estimate is not completely solved in multivariate case. This work proposes a new constructive a few stage procedure to solve this task. This procedure includes statistical distribution analysis of a large number of the univariate projections of observations, geometric clustering of a multivariate sample and application of EM algorithm. The results of the accuracy analysis of the proposed methods is made by means of Monte-Carlo simulation.
BackgroundThis study aimed to assess the trends in the prevalence of electrocardiographic (ECG) abnormalities from 1986 to 2015 and impact of ECG abnormalities on risk of death from cardiovascular diseases (CVD) in the Lithuanian population aged 40–64 years.MethodsData from four surveys carried out in Kaunas city and five randomly selected municipalities of Lithuania were analysed. A resting ECG was recorded and CVD risk factors were measured in each survey. ECG abnormalities were evaluated using Minnesota Code (MC). Trends in age-standardized prevalence of ECG abnormalities were estimated for both sexes. Multivariate Cox proportional hazards models were used to estimate hazard ratios (HR) for coronary heart disease (CHD) and CVD mortality. Net reclassification index (NRI), integrated discrimination improvement and other indices were used for evaluation of improvement in the prediction of CVD and CHD mortality risk after addition of ECG abnormalities variable to Cox models.ResultsFrom1986 to 2008, the decrease in the prevalence of Q-QS MC was observed in both genders. The prevalence of high R waves increased in men, while the prevalence of ST segment and T wave abnormalities as well as arrhythmias decreased in women. Ischemic changes and possible MI were associated with a 2.5-fold and 4.4-fold higher risk of death from CVD in men and 1.51-fold and 2.56-fold higher mortality risk from CVD in women as compared to individuals with marginal or no ECG abnormalities. The addition of ECG abnormalities to traditional CVD risk factors improved Cox regression models performance. According to NRI, 18.6% of men were correctly reclassified in CVD mortality prediction model and 25.2% of men - in CHD mortality prediction model.Conclusionsthe decreasing trends in the prevalence of ischemia on ECG in women and increasing trends in the prevalence of left VH in men were observed. ECG abnormalities were associated with higher risk of CVD mortality. The addition of ECG abnormalities to the prediction models modestly improved the prediction of CVD mortality beyond traditional CVD risk factors. The use of ECG as routine screening to identify high risk individuals for more intensive preventive interventions warrants further research.
Consumer lifestyle is considered one of the important predictors of sustainable consumption behavior at the individual, community and societal levels. In this paper, the healthy lifestyle of consumers is analyzed and defined as the lifestyle that explains how people live in terms of health. This study focuses on consumers’ healthy lifestyle clusters and offers an updated healthy lifestyle measurement tool that can be used to segment consumers into specific segments according to six healthy lifestyle domains: physical, mental, emotional, social, spiritual and intellectual health. An online survey with 645 respondents of different socio-demographic profiles was conducted in Lithuania. Based on data collected through questionnaires, specific segments were identified using self-organizing maps and cluster analysis methods. The findings suggest that four different segments could represent consumers concerning their healthy lifestyles. The results will be of use to companies initiating marketing campaigns to target different consumer groups with their brands and offering healthy lifestyle-related products and services to consumers in Lithuania. The findings are also valuable for public policymakers and opinion leaders who foster healthy lifestyles and seek to form a public opinion regarding sustainable consumption.
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